{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import tensorflow as tf\n",
    "from scipy.stats import mvn, norm\n",
    "import itertools\n",
    "marker = itertools.cycle((',', '+', '.', 'o', '*'))\n",
    "from IPython.core.pylabtools import figsize\n",
    "figsize(15, 4)\n",
    "pd.options.display.max_colwidth = 60\n",
    "from pprint import pprint\n",
    "\n",
    "def np_cdf(mean, diag_sigma, value, name=None):\n",
    "    low = np.array([-30, -30])\n",
    "    cdf = list()\n",
    "    for s in value:\n",
    "        # mvn.mvnun(low, upp, mean, cov)\n",
    "        p, _ = mvn.mvnun(low, upper=s, covar=diag_sigma, means=mean)\n",
    "        cdf.append(p)\n",
    "    cdfs = np.asarray(cdf, dtype=np.float32).reshape([-1, 1])\n",
    "    return cdfs\n",
    "\n",
    "def cartesian(arrays, out=None):\n",
    "    \"\"\"\n",
    "    Generate a cartesian product of input arrays.\n",
    "\n",
    "    Parameters\n",
    "    ----------\n",
    "    arrays : list of array-like\n",
    "        1-D arrays to form the cartesian product of.\n",
    "    out : ndarray\n",
    "        Array to place the cartesian product in.\n",
    "\n",
    "    Returns\n",
    "    -------\n",
    "    out : ndarray\n",
    "        2-D array of shape (M, len(arrays)) containing cartesian products\n",
    "        formed of input arrays.\n",
    "\n",
    "    Examples\n",
    "    --------\n",
    "    >>> cartesian(([1, 2, 3], [4, 5], [6, 7]))\n",
    "    array([[1, 4, 6],\n",
    "           [1, 4, 7],\n",
    "           [1, 5, 6],\n",
    "           [1, 5, 7],\n",
    "           [2, 4, 6],\n",
    "           [2, 4, 7],\n",
    "           [2, 5, 6],\n",
    "           [2, 5, 7],\n",
    "           [3, 4, 6],\n",
    "           [3, 4, 7],\n",
    "           [3, 5, 6],\n",
    "           [3, 5, 7]])\n",
    "\n",
    "    \"\"\"\n",
    "\n",
    "    arrays = [np.asarray(x) for x in arrays]\n",
    "    dtype = arrays[0].dtype\n",
    "\n",
    "    n = np.prod([x.size for x in arrays])\n",
    "    if out is None:\n",
    "        out = np.zeros([n, len(arrays)], dtype=dtype)\n",
    "\n",
    "    m = n / arrays[0].size\n",
    "    out[:,0] = np.repeat(arrays[0], m)\n",
    "    if arrays[1:]:\n",
    "        cartesian(arrays[1:], out=out[0:m,1:])\n",
    "        for j in range(1, arrays[0].size):\n",
    "            out[j*m:(j+1)*m,1:] = out[0:m,1:]\n",
    "    return out"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/mp74207/anaconda/envs/snow35/lib/python3.5/site-packages/ipykernel/__main__.py:67: VisibleDeprecationWarning: using a non-integer number instead of an integer will result in an error in the future\n",
      "/Users/mp74207/anaconda/envs/snow35/lib/python3.5/site-packages/ipykernel/__main__.py:69: VisibleDeprecationWarning: using a non-integer number instead of an integer will result in an error in the future\n"
     ]
    },
    {
     "data": {
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XV+crnU7XnSiL5a0uBsR8fluHq9y9JiRouF+Fi/mimoRPK7/XfqWVqrjy2zlQnian7pnn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\noy5RD+ymunbtmhISEoYNp4a7jo2NDQqfR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      "text/plain": [
       "<matplotlib.figure.Figure at 0x11092d8d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "from matplotlib import cm\n",
    "from matplotlib.ticker import LinearLocator\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "\n",
    "low = np.array([-10, -10])\n",
    "upp = np.array([.1, -.2])\n",
    "mean = np.array([0, 1])\n",
    "cov = np.array([(1, .5), (.5, 1)])\n",
    "\n",
    "fig = plt.figure()\n",
    "ax = fig.gca(projection='3d')\n",
    "X0 = np.arange(-5, 5, 0.25)\n",
    "xlen = len(X0)\n",
    "Y0 = np.arange(-5, 5, 0.25)\n",
    "ylen = len(Y0)\n",
    "X, Y = np.meshgrid(X0, Y0)\n",
    "data = cartesian(arrays=[X0, Y0])\n",
    "# init(data, low, upp, 5, 20)\n",
    "Z = np_cdf(mean=mean, diag_sigma=cov, value=data, name=None).reshape([xlen,ylen])\n",
    "\n",
    "colortuple = ('y', 'b')\n",
    "colors = np.empty(X.shape, dtype=str)\n",
    "for y in range(ylen):\n",
    "    for x in range(xlen):\n",
    "        colors[x, y] = colortuple[(x + y) % len(colortuple)]\n",
    "\n",
    "surf = ax.plot_surface(X, Y, Z, rstride=1, cstride=1, facecolors=colors,\n",
    "                       linewidth=0, antialiased=False)\n",
    "\n",
    "ax.set_zlim3d(-1, 1)\n",
    "ax.w_zaxis.set_major_locator(LinearLocator(6))\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Question\n",
    "\n",
    "I am reviewing this Tuesday’s slide. In page 11(lecture 9), the tranche notional is calculated as J(K1,K2)=Q(K1,K2,T)*(K2-K1). I do not quite understand what this notional mean. \n",
    "\n",
    "According to page 9, tranche notional loss = E[min(LT,K2)]-E[min(LT,K1)]. Is this notional the same one as J(K1,K2)?\n",
    "\n",
    "If they are the same, then J(K1,K2)=[1-Q(K1,K2,T)] * (K2-K1), by using Q(K1,K2,T) = 1-{E[min(LT,K2)]-E[min(LT,K1)] / (K2-K1)}. Is this right?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "R=0.4\n",
    "PD= 0.05 # Probability of default per year \n",
    "PD = np.array([0.05*x for x in range(1,100) ]) # Probability of default per year\n",
    "beta = 0.3\n",
    "CT = norm.ppf(PD)\n",
    "x = 0.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def AA(CT,x,R):\n",
    "    AAA = CT - np.sqrt(1-beta*beta)*norm.ppf(x/(1-R))\n",
    "    AAA[AAA < -10]=-10\n",
    "    AAA[AAA > 10] = 10\n",
    "    return AAA"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Notice that Emin is multiplied by the total notional of the tranche K!!!!\n",
    "# $AA(K)) = \\frac{C(T)-\\sqrt({1-\\beta^2})\\phi(\\frac{K}{(1-R)})}{\\beta}$\n",
    "# $E[min(L_T,K)] = K*[(1-R)*\\Phi_2^{-1}(C(T),-AA(K),-\\beta)+\\Phi(AA(K)]$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def Emin(K,R,CT,beta):\n",
    "    mean=np.array([0,0])\n",
    "    cov = np.array([[1,-beta],[-beta,1]])\n",
    "    AAK = AA(CT=CT,x=K,R=R)\n",
    "    upp = np.array([(x,y) for x,y in zip(CT,-AAK)])\n",
    "    A = np_cdf(mean=mean, diag_sigma=cov, value=upp, name=None)\n",
    "    A = np.asarray(A, dtype=np.float32).reshape([-1, 1])\n",
    "    B = norm.cdf(AAK)\n",
    "    B = np.asarray(B, dtype=np.float32).reshape([-1, 1])\n",
    "    return K*((1-R)*A + B)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def Q(K1,K2,CT,R,beta):\n",
    "    QQ1 = Emin(K=K1,R=R,CT=CT,beta=beta)\n",
    "    QQ2 = Emin(K=K2,R=R,CT=CT,beta=beta)\n",
    "    QQ =1- (QQ2-QQ1)/(K2-K1)\n",
    "    return QQ,QQ1,QQ2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/mp74207/anaconda/envs/snow35/lib/python3.5/site-packages/ipykernel/__main__.py:3: RuntimeWarning: invalid value encountered in less\n",
      "  app.launch_new_instance()\n",
      "/Users/mp74207/anaconda/envs/snow35/lib/python3.5/site-packages/ipykernel/__main__.py:4: RuntimeWarning: invalid value encountered in greater\n",
      "/Users/mp74207/anaconda/envs/snow35/lib/python3.5/site-packages/scipy/stats/_distn_infrastructure.py:875: RuntimeWarning: invalid value encountered in greater\n",
      "  return (self.a < x) & (x < self.b)\n",
      "/Users/mp74207/anaconda/envs/snow35/lib/python3.5/site-packages/scipy/stats/_distn_infrastructure.py:875: RuntimeWarning: invalid value encountered in less\n",
      "  return (self.a < x) & (x < self.b)\n",
      "/Users/mp74207/anaconda/envs/snow35/lib/python3.5/site-packages/scipy/stats/_distn_infrastructure.py:1731: RuntimeWarning: invalid value encountered in greater_equal\n",
      "  cond2 = (x >= self.b) & cond0\n"
     ]
    }
   ],
   "source": [
    "K1=0.03\n",
    "K2 = 0.06\n",
    "R=0.4\n",
    "beta=0.3\n",
    "QQ,QQ1,QQ2= Q(K1,K2,CT,R,beta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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aOf61T5IkKdv8G5kkSdJ+YsWmFaWLKkz6aBIzPplBJNK2UVsGdxzM5cdczuCO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\nAyEOAAAAAAYBveoeSrYjwLoAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11096e6d8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x=CT\n",
    "fig = plt.figure()\n",
    "fig.suptitle('CDO Tranche Loss Function', fontsize=14, fontweight='bold')\n",
    "ax = fig.add_subplot(111)\n",
    "ax.set_xlabel('CDO Tranche Loss versus Default Barrier Height')\n",
    "ax.set_ylabel('Accumulated Tranche Loss')\n",
    "ax.plot(x,QQ1)\n",
    "ax.plot(x,QQ2)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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z00mSJEmSNHuzyCb1MgsvDCecAI88AhtuWFq5Lb88XHwxTJ3a7HSSJEmSJM2e\nLLJJvdQSS8C558I998CgQWX8tpbZSSVJkiRJUsdYZJN6uSFD4Mor4cYbYY45Suu2DTeE8eObnUyS\nJEmSpNmHRTZJAKy9NtxyC1x+OTz3HKy8MmyzDTz2WLOTSZIkSZLU/Vlkk/SRCNh8c7jvPvjd7+DW\nW8t4bd//Pjz/fLPTSZIkSZLUfVlkk/QxffvCTjvBo4/CUUeVSRGWWQaOOQY++KDZ6SRJkiRJ6n4s\nsklq08CBsP/+8OSTsOuucNBBMHQoXH99s5NJkiRJktS9WGSTNFPzzQejR8OECbDQQvCVr5TZSJ99\nttnJJEmSJEnqHiyySWq3IUPKLKTnngs33ADLLQfHHQeTJzc7mSRJkiRJzdXhIltELBgRv42IJyPi\nrYh4p3rpipCSuo8I+M53YOJEGDkSfvxjWHHFUnSTJEmSJKm3qqcl21hgXeBkYBdgp5pFUi8w33xw\n0kmlC+l888H668P228NzzzU7mSRJkiRJs16/Oo5ZF1gvMyc0Ooyk2c/QoXDTTXDeefCjH5UupIcd\nBnvtBf37NzudJEmSJEmzRj0t2Z4DpjQ6iKTZV58+sMMO8Oij5ef++8OwYWX8NkmSJEmSeoN6imz7\nAUdFxKcbGSQi9oyIpyLi3Yi4PSJWmcn+80bEbyLiucoxEyPiq43MJKlj5psPTj4Z7roL5p4b1l23\njN/2wgvNTiZJkiRJUteqp8h2JrA+8H8R8XKlyPXRUk+IiNgGOB44FFgJuBe4JiIWamP//sC1wOeA\nrYBBwPeAZ+u5vqTGWmkluOUWOOss+OtfYdCgMn7bhx82O5kkSZIkSV2jnjHZft7oEMAo4PTMPBcg\nInYHNgNGAse0sv/OwHzAlzKzpevqM12QS1Kd+vQps49usQUcfDCMGgW/+x385jew1lrNTidJkiRJ\nUmN1uMiWmac3MkClVdpw4Miqa2REXAus3sZhXwduA06JiM2Bl4ELgaMzc2oj80nqnAUWgFNOgZ13\nhj32gLXXhu9+F445Bj75yWankyRJkiSpMerpLkoUm0XE/hGxX0RsEhFRZ4aFgL7AizXrXwQ+1cYx\nSwL/S8m/CfALylhxB9WZQVIXGz4cbrsNfvtb+MtfShfSX//aLqSSJEmSpJ6hw0W2iFgCuB/4A6U7\n5y7A5cC9EbF4A7MFkG1s60Mpwu2amXdn5iXAEcD3G3h9SQ3Wpw/ssgs88ghsuy3ssw+ssgrcemuz\nk0mSJEmbSyThAAAgAElEQVSS1Dn1jMl2MvAC8JXMfBEgIj4FXACMATbv4PleAaYAtR3HFuHjrdta\nPA98kJnVRbiHgU9FRL/MbLNtzKhRo5h33nmnWzdixAhGjBjRwdiS6rXggnDaadO6kK65Juy0E/zq\nV7DIIs1OJ0mSJEnqScaNG8e4ceOmWzdp0qSGXyemr1O144CIt4A1MvO+mvUrAjdl5jwdDhFxO3BH\nZu5beR+UiQzGZOaxrex/BDAiM5esWrcv8KPMXKyNawwDxo8fP55hw4Z1NKKkLjJlSpmF9MADYepU\nOOII2G036Nu32ckkSZIkST3VhAkTGD58OMDwzJzQiHPWMybbh8DAVtbPWdlWj9HArhHx3YhYDjgN\nmAsYCxAR50bEkVX7nwosGBEnRcQyEbEZcCDw6zqvL6lJ+vaFXXctXUj/939hzz1h1VXh9tubnUyS\nJEmSpParp8h2FXBaRAxtWVFpxXYq8Jd6QlTGVNsPOBy4GxgCbJyZL1d2WYyqSRAy8/+AjYBVgHuB\nE4ETgKPrub6k5ltoITjjjGnFtdVXL+O3vfzyjI+TJEmSJKk7qKfItjfwEnB3RLxV6T46njJO2z71\nBsnMUzJzicwcmJmrZ+ZdVdu+nJkja/a/IzPXyMy5MnOZzDw6O9r3VVK3s9pqcOedcMopcNllZRbS\n004r3UolSZIkSequOlxky8xXM3NjYCiwE2WG0aGZuUlm/rfRASX1Pn37wve/D48+CltuWV63FN8k\nSZIkSeqO6mnJBkBm3p+Zl2bmJZn5QCNDSRLAwguXSRFuvbW0ZPvSl8r4ba++2uxkkiRJkiRNr197\ndqpMOvDLzHynZgKCj8nMgxqSTJIqVl8d7rqrdBv96U9LN9KjjipjtvWp+38VSJIkSZLUOO399XR9\nYEDV67aW9RqcT5KA0oV0zz1LF9JvfAN22620bLvrrpkfK0mSJElSV2tXka0yEcHrVa/bWtbo2riS\nertFFoGzz4abb4YPPoBVVy1jtv3XESElSZIkSU3U4Y5WEXFKRMzdyvq5IuKUxsSSpBlbc83Siu2k\nk+DCC2HZZcv4bVOnNjuZJEmSJKk3qmc0o92AuVpZPxewa+fiSFL79esHe+8NjzwCm25axmhbYw2Y\nMKHZySRJkiRJvU27i2wRMSAi5gACGFB537IMBL4MvNJVQSWpLZ/6FJx7Lvzzn/DOO7DyymX8ttde\na3YySZIkSVJv0ZGWbO8B7wAJPA28W7W8BYwDzmh0QElqr3XWKa3YRo+G886DQYPK+G12IZUkSZIk\ndbWOFNk2ATajtGTbHti0atkAWDozf9bwhJLUAf36wQ9+ULqQbrQRjBwJa60F99zT7GSSJEmSpJ6s\n3UW2zLwmM/8KDAYurrxvWf6RmU91XUxJ6phPfxrOPx9uuAHeeAOGDy/jt73+erOTSZIkSZJ6onom\nPlgZ2LJ2ZURsFREjOh9Jkhpn3XXh7rvh2GNh7NjShfSccyCz2ckkSZIkST1JPUW2Q4A3Wln/GmB3\nUUndTv/+8MMfli6kX/kK7LhjGb/tvvuanUySJEmS1FPUU2RbAni8lfVPAYt3Ko0kdaFFF4ULL4Tr\nr4dXX4Vhw8r4bZMmNTuZJEmSJGl2V0+R7WVghVbWfwFwtCNJ3d7665eJEH71KzjzzNKF9Pzz7UIq\nSZIkSapfPUW2S4AxEbF6y4qIWAM4qbJNkrq9AQNg//1h4sQybtt3vlN+3n9/s5NJkiRJkmZH9RTZ\nfgo8ANwSEW9HxNvATcAdwIGNDCdJXW2xxeDii+Hvf4eXXoKVVirjt73R2siTkiRJkiS1ocNFtsx8\nLzM3B4YCuwM7AIMzc7vMfLfRASVpVthggzIRwhFHwOmnly6kF15oF1JJkiRJUvvU05INgMy8PzPP\ny8zfZ+ajjQwlSc0wYAD8+MelC+laa8H225fx2x58sNnJJEmSJEndXYeLbFFsHxG/i4grI+Kq6qUr\nQkrSrPTZz8Kll8I118Dzz8OKK5bx2958s9nJJEmSJEndVT0t2UYDZwILAv8HPF2zSFKPsNFGpQvp\n4YfDKafAcsuV8dvsQipJkiRJqtWvjmO2B7bJzCsaHUaSups55oADD4TttisTImy7LZxxBvz61zB4\ncLPTSZIkSZK6i3pask0FHm50EEnqzhZfHC67DK6+Gp55BoYMKeO3vfVWs5NJkiRJkrqDeopsJwF7\nNDqIJM0OvvpVuP9+OPRQGDOmdCG99FK7kEqSJElSb1dPkW0IsGNETIyISyPiwuql0QElqbuZc044\n+GB4+GFYeWX41rdg443hUedZliRJkqReq54iG8BfgbuBD4GoWSSpV1hiCbj8crjySnj8cfjiF+GQ\nQ+Cdd5qdTJIkSZI0q3V44oPMHNEVQSRpdrXZZvDlL8NRR8HRR8P558PJJ8PXvtbsZJIkSZKkWaXe\nlmySpCoDB8Lhh8MDD8Cyy8LXvw5bbAFPP93sZJIkSZKkWaHDRbaIeDgiHmprqTdIROwZEU9FxLsR\ncXtErDKDfXeIiKkRMaXyc2pE2EFLUtMtswz89a9lMoS77oLBg0sLtw8+aHYySZIkSVJXqqcl21jg\nnKrlQuBh4FPARfWEiIhtgOOBQ4GVgHuBayJioRkcNqlyzZZl8XquLUmNFgFbb10mRthjjzJO25Ah\ncN11zU4mSZIkSeoq9YzJdnRr6yPiB8AKdeYYBZyemedWzrU7sBkwEjim7Sj5cp3Xk6QuN888cNxx\nsMMOsOeesMEGsO22cPzxsOiizU4nSZIkSWqkRo7J9mfgWx09KCL6A8OBj9p4ZGYC1wKrz+DQuSPi\n3xHxTERcHhHLd/TakjQrfPGL8M9/wjnnlNZsyy0HJ50EH37Y7GSSJEmSpEZpZJHta5QunB21ENAX\neLFm/YuUbqCteYTSyu0bwPaU+7g1Ij5Tx/UlqctFwHe/C488At/5DowaBSuvDLfe2uxkkiRJkqRG\nqGfig9si4taq5baI+Dcwmra7dtYjgGxtQ2benpnnZ+Z9mXkTsBXwMrBrA68vSQ03//zwm9/AnXfC\ngAGw5pqw887wyivNTiZJkiRJ6owOj8kG3FDzfiqlwHV9Zt5Xx/leAaYAn6xZvwgfb93Wqsz8MCLu\nBpae2b6jRo1i3nnnnW7diBEjGDFiRPvSSlIDrLwy3HYb/Pa3cOCBcPnlZRbSXXaBPo1sYyxJkiRJ\nvdy4ceMYN27cdOsmTaqnM+aMRRn+rLki4nbgjszct/I+gGeAMZl5bDuO7wM8AFyVmfu3sc8wYPz4\n8eMZNmxY48JLUie99BL8+Mcwdiysthqccgr415QkSZIkdZ0JEyYwfPhwgOGZOaER52x3e4mIOCgi\nBla9Hzij/TtoNLBrRHw3IpYDTgPmAsZWrnVuRBxZde1DImLDiPh8RKwEXAAsDpzZwEySNEsssgic\nfTbcdBO8/TassgrsvTe8/nqzk0mSJEmS2qsjnZJ+AcxT9f7FiFiyESEy8xJgP+Bw4G5gCLBxZr5c\n2WUxpp8EYX7gDOAh4C/A3MDqmTmxEXkkqRnWWgsmTIBjjy2t2pZbDs4/H7pBg2NJkiRJ0kx0pMgW\nM3nfKZl5SmYukZkDM3P1zLyratuXM3Nk1fsfZubnK/sumplfr3M8OEnqVvr3hx/+ECZOhHXXLTOR\nrr8+PPRQs5NJkiRJkmbE4bUlqRv6zGfg4ovhb3+D556DoUPLuG1vvdXsZJIkSZKk1nSkyJbAgIgY\nEBFzVN73r7z/aOmamJLUO224Idx/Pxx6KIwZA8svD3/4g11IJUmSJKm76Wh30aeBd4F3KOOgPVR5\nX71Ikhpojjng4INLl9GhQ+Gb34TNNoMnnmh2MkmSJElSi34d2HeTLkshSZqpz38e/vxnuOIK2Gcf\nWGEFOPDA0o10zjmbnU6SJEmSerd2F9ky85quDCJJap9vfAM22ACOOKIs550HJ58Mm/i/QiRJkiSp\naZz4QJJmQ3PNVQps990HSywBm25aupH+5z/NTiZJkiRJvZNFNkmajS23HPz97zBuHNx2GwweDMce\nC5MnNzuZJEmSJPUuFtkkaTYXAdtuCxMnwve+Bz/5Cay4Ivzzn81OJkmSJEm9h0U2SeohPvEJOOEE\nmDAB5psP1lsPvvMdeOGFZieTJEmSpJ7PIpsk9TBDh8JNN8FZZ8HVV5cupb/+NUyZ0uxkkiRJktRz\ntWt20Yi4sL0nzMzt6o8jSWqEPn1g5EjYfHM46CDYZx84+2w45RRYbbVmp5MkSZKknqe9LdmiA4sk\nqZtYcEE4/fQyKUImrL467LYbvPpqs5NJkiRJUs/SrpZsmTmiq4NIkrrOaqvBv/4Fp50GP/0pXHYZ\nHHMM7LhjafUmSZIkSeocf7WSpF6ib1/Yc88yC+kmm8DOO8Paa8O99zY7mSRJkiTN/uoqskXE1yLi\n3Ii4ISJurV4aHVCS1Fif+hScdx784x/w+uswfDiMGgVvvNHsZJIkSZI0++pwkS0ivg9cDLwPrA48\nAkwBlgduaWg6SVKXWW89uPtuOPJIOOOMMgvpRReVsdskSZIkSR1TT0u2fYDdM/N7wAfALzJzbeA0\noH8jw0mSutaAAXDAAaUL6RprwIgRsMEG5b0kSZIkqf3qKbItDtxYef0eME/l9VnA9o0IJUmatT77\nWfj97+Gqq+Dpp2HIkDJBwjvvNDuZJEmSJM0e6imyvQTMX3n9DLBy5fVnaedspZKk7mmTTeCBB0qB\n7fjjYfnl4Yormp1KkiRJkrq/eops/wC+Vnl9HnBSRPwZuAT4c6OCSZKaY8454dBD4cEHYfBg2Hxz\n+NrX4PHHm51MkiRJkrqveopsuwGjATLzRGAv4HngaGDXxkWTJDXTUkuV7qOXXQb33w8rrAAHHghv\nvdXsZJIkSZLU/XS4yJaZH2TmO1Xvx2bmrpl5bGa+19h4kqRmioCttoKHH4aDDoITT4RBg+D8852F\nVJIkSZKqdbjIFhEPRMSPI2LxrggkSep+5pqrdCGdOBHWXBO+8x1Yay0YP77ZySRJkiSpe6inu+iF\nlFlEn4yIGyNi14hYoMG5JEnd0OKLwyWXwPXXwxtvwCqrwK67wssvNzuZJEmSJDVXPd1Fj8zMIcBK\nwG3AQcBzEfGniPhWowNKkrqf9deHu++GMWPg97+HZZaBk06CyZObnUySJEmSmqOelmwAZOZ9mfnj\nzFwC2Aj4HDCuUcEkSd1bv36w117w6KMwYgSMGgUrrgjXXtvsZJIkSZI069VdZAOIiCER8SvgPGB5\n4MqGpJIkzTYWWghOPbWMz7bAArDhhmWyhKeeanYySZIkSZp16pn4YPGIODAi7gfuBtYAjgQ+lZmb\nNzqgJGn2sNJKcOONcOGFcOedMHgw/Oxn8PbbzU4mSZIkSV2vnpZsTwEjgAuAz2fmOpl5ema+1pkg\nEbFnRDwVEe9GxO0RsUo7j9s2IqZGxB86c31JUudFlK6jjzwC++8PxxwDyy0HF18Mmc1OJ0mSJEld\np54i24qZOSQzf5WZzzQiRERsAxwPHEqZUOFe4JqIWGgmxy0OHAvc2IgckqTG+J//gV/+Eh56CFZe\nGbbdFtZbD+69t9nJJEmSJKlr1DO76H1dkGMUcHpmnpuZE4HdgXeAkW0dEBF9gPOBn1Fa10mSupkl\nl4Q//hGuuQZeegmGDYM99oBXX212MkmSJElqrHYV2SLiuYhYsPL6+cr7VpeOBoiI/sBw4LqWdZmZ\nwLXA6jM49FDgpcw8u6PXlCTNWhttBPfdB8cfDxdcAMssA6ecAh9+2OxkkiRJktQY/dq532HAW1Wv\nGzmyzkJAX+DFmvUvAoNaOyAi1gR2AoY2MIckqQv17w8/+AFstx0cdBDstRecdhqMGVO6kkqSJEnS\n7KxdRbbMPL3q9WldF2c6QSvFvIiYGzgP+F5nJ1uQJM16iywCZ54Ju+8Oe+8N668P3/oWHHssfO5z\nzU4nSZIkSfVpb0u2j0TEnyljoV2Rme82IMMrwBTgkzXrF+HjrdsAlgIWB/4cEVFZ16eS7QNgUGa2\nOUbbqFGjmHfeeadbN2LECEaMGFFfeklSXVZeGW65pXQfPeCAMgvpT34CP/oRDBzY7HSSJEmSeopx\n48Yxbty46dZNmjSp4deJMvxZBw6IOAPYChgAXE4puF2bmVPrDhFxO3BHZu5beR/AM8CYzDy2Zt8B\nwNI1pzgCmBvYB3gsMz82yk9EDAPGjx8/nmHDhtUbVZLUBd58E444AkaPhkUXLWO3bbUVfPS/UiRJ\nkiSpgSZMmMDw4cMBhmfmhEacs57ZRXcFPgV8m1Jo+yPwXEScFBGr1ZljNLBrRHw3IpYDTgPmAsYC\nRMS5EXFk5fofZOZD1QvwOvBmZj7cWoFNktS9zTMP/OpX8OCD8IUvwNZbwwYbwAMPNDuZJEmSJLVP\nh4tsAJn5YWZekZnbUrp5/ghYD7ilzvNdAuwHHA7cDQwBNs7Mlyu7LEYp7EmSerBlloErryzLf/4D\nK64I++4LrzkCpyRJkqRurq4iW4uIWIDSom034AvAg/WeKzNPycwlMnNgZq6emXdVbftyZo6cwbE7\nZeZW9V5bktS9bLZZacV21FHwu9/BssvCGWfAlCnNTiZJkiRJretwkS0iBkbEiMoECM8DPwFuAoZm\n5tBGB5Qk9U4DBpRJEB59FDbdFHbbDVZZpUyWIEmSJEndTT0t2V4GxgDPAhtUWp8dmJmOnCNJarhP\nfxrOOQduuw369oW11oLtt4dnn212MkmSJEmapkNFtsqsn3sAn8nM3TPzpq6JJUnS9L70JbjjDjjr\nLLj2Whg0qHQnfe+9ZieTJEmSpI63ZAvgTODzXZBFkqQZ6tMHRo4sXUh32w1+9rMyG+kVV0Bms9NJ\nkiRJ6s06VGTLzKnAk8AnuiaOJEkzN++8cPzxcN99sNRSsPnmsMkmMHFis5NJkiRJ6q3qGZPtIODY\niFi60WEkSeqIwYPhr3+Fyy+Hxx6DL34R9tsPJk1qdjJJkiRJvU09RbbfAKsBj0TEpIh4rnppcD5J\nkmYoorRke/BBOOwwOO00WHZZOPtsmDq12ekkSZIk9Rb96jjm540OIUlSZ805Jxx0EHz3u3DAAWXs\ntlNPhZNPhtVWa3Y6SZIkST1dh4tsmXl6VwSRJKkRFlsMLrwQvv992GefMivpDjvAkUfCoos2O50k\nSZKknqrD3UUjYpEZLV0RUpKkjlp7bbjrrtJ99MorYeml4ZBD4I03mp1MkiRJUk9Uz5hsLwDPz2CR\nJKlb6NsXdtsNHn8c9t0XjjuuFNt+8xuYPLnZ6SRJkiT1JPUU2VYH1qha1gV+ADwJjGhcNEmSGmO+\n+eCoo+DRR2GzzWDvvWGFFeCyyyCz2ekkSZIk9QQdLrJl5h01y82ZeTKwP7Bb4yNKktQYn/1smXX0\nnntgqaVg661hjTXg5pubnUySJEnS7K6elmxteRD4UgPPJ0lSlxgyBK6+Gv7+d3j//TJ+25ZbwsSJ\nzU4mSZIkaXZVz8QHA2qWOSJiCeBnwBONDihJUlfZYIMyOcL558Pdd8MXvlBmJX3hhWYnkyRJkjS7\nqacl23vAu1XLO5Ti2gbAXo2LJklS1+vTB7bfvrRiO/pouOiiMjnCYYfBW281O50kSZKk2UU9RbZN\ngE2rlq8Cw4ElMvPGBmaTJGmWmXNO2G8/eOKJ0prtyCNLse300+HDD5udTpIkSVJ3V8/EB9fULH/P\nzHsy84OuCChJ0qy0wAJw7LFlJtINN4Tddy/dSP/0J2cilSRJktS2dhfZImLJiFipZt3aEXF1RNwY\nET9sfDxJkppj8cXhvPNgwgRYbDHYYgtYZx24/fZmJ5MkSZLUHXWkJduxwNYtbyLic8DVwEDgYeCX\nEeGYbJKkHmWllcospH/9K7zxBqy+Omy9NTz2WLOTSZIkSepOOlJkWwW4qur9t4GnMnO9zNwNGAWM\nbGQ4SZK6gwjYeOPSqm3sWLjzTlh+edhrL3jppWankyRJktQddKTItjDwn6r36wNXVL2/DliyEaEk\nSeqO+vaFHXaARx6BI46A88+HpZaCX/4S3n672ekkSZIkNVNHimyvAYsARERQWrZVj0zTD4jGRZMk\nqXsaOBAOOKDMRPq978Hhh8Myy8CZZzoTqSRJktRbdaTIdiNwUEQsDOwB9AduqNo+GHimcdEkSere\nFlwQRo+GiRNhvfVKwW3oULjySmcilSRJknqbjhTZfgqsBLwAnAQclJlvVm3/NnB9A7NJkjRbWHJJ\n/r+9+w6zqyz3Pv690ykSeu8gvSZ0FFAQjyggx0ZE5T2giIIiRVAsKFIUkSZFEaUIBDgeBRQQpAtS\nQoIUCUUIvYUWkJ7kfv941jA7k2l72p7y/VzXujJ77Wetfa/Mmj0zv3kK558PkybB4ovDjjvChz5U\nHkuSJEkaGjodsmXmw5TealsAq2bmiS2aHAMc2YO1SZI0oGy0EVx7LVx2GbzwAmyyCey6axlWKkmS\nJGlwq6cnG5n5VmbelpmPtvLcbZnpGmuSpCEtAnbYAe66C377W/j732HNNeFb3yrBmyRJkqTBqa6Q\nTZIkdc7w4bDHHvDQQ/CjH8HvfldWIv3pT+HNNxtdnSRJkqSe1m9CtojYJyKmRcSbEXFrRGzcTttd\nImJSRLwcEf+JiDsj4gt9Wa8kSZ0x77xw6KFlyOjuu8MPfgCrrQZnnQWzZjW6OkmSJEk9pV+EbBHx\nOeAXwGGUxRXuAq6MiEXbOORF4AhgM2Bd4EzgzIj4SB+UK0lS3RZbDE46CaZOhc03h//5H9hwQ7ji\nClcilSRJkgaDfhGyAfsDv87MczLzfmBv4A1gj9YaZ+aNmXlJZj6QmdMy8yTgbuADfVeyJEn1W3VV\nuOgiuPVWWHDBMn/bdtvB5MmNrkySJElSd3QpZIuITSLijIi4LiKWrvbtGhGbdeFcI4HxwDVN+zIz\ngauBzTt5jm2B1YAb6n19SZIaYdNN4YYb4JJL4Omny8qku+0Gjz7a6MokSZIkdUXdIVtE7EQJs0ZT\nQrAx1VOLA9/vQg2LAsOB51rsfw5Ysp06FoiI1yLiHeDPwDcy89ouvL4kSQ0RATvtBPfcA7/+NVx7\nLay+OhxwADzvet2SJEnSgDKiC8ccBuybmb+NiE/W7L8J+G7PlAVAAO3NUvMasD4wP7AtcHxEPJKZ\nN7Z30v3335+xY8fOsW/ChAlMmDChm+VKktQ1I0bAXnuVnmzHHQfHHFNCt332gYMOgsUXb3SFkiRJ\n0sA1ceJEJk6cOMe+GTNm9PjrRNY523JEvA6snZmPRsRrwPqZ+UhErAzcl5ljOjhFy/ONpMy/9qnM\nvLRm/1nA2MzcpZPn+Q2wbGZ+rI3nxwGTJ0+ezLhx4+opUZKkPvXii3D88XDiiTB7tmGbJEmS1NOm\nTJnC+PHjAcZn5pSeOGdX5mR7Hliplf2bA9PqPVlmvgtMpvRGAyAionr8jzpONYwyhFWSpAFtkUXg\niCPK/Gz77w+nnQYrrQQHH+wwUkmSJKm/6krIdiZwQkSsTxnOuUhEfAo4Fji9i3UcB+wVEV+KiDWA\nXwHzAmcBRMQ5EXFUU+OI+E5EbBcRK0XEGhFxIPAF4PddfH1JkvodwzZJkiRp4OhKyHYEcClwC2U+\ntFuB84FzM/P4rhSRmRcBBwKHA3cC6wEfzczpVZNlmXMRhPmAU4B7KXPB7QLslplnduX1JUnqzwzb\nJEmSpP6v7jnZ3jswYj5gdUrQdk9mvtyThfU052STJA0WztkmSZIkdU9/mZMNgMx8PTOnZOaN/T1g\nkyRpMKnt2fatbzX3bDvkEJg+vcPDJUmSJPWCukO2iJgnIr4XEddGxL0RcV/t1htFSpKkuS2yCBx5\nZHPYduqpsOKKhm2SJElSI3SlJ9uvgf2Ae4BzgbNbbJIkqQ8ZtkmSJEmNN6ILx+wIfDIzb+jpYiRJ\nUtc1hW0HHADHHQcnnQQnnwz77lvmbFtssUZXKEmSJA1eXenJ9irgWmaSJPVT9myTJEmS+l5XQrYf\nAT+IiNE9XIskSepBhm2SJElS3+lUyBYRt0TEPyLiH8BXgI8Dz0bEpKb9Nc9LkqR+pLWwbaWV4Dvf\nMWyTJEmSekpn52S7vsVj52OTJGmAaW/OtgMPdM42SZIkqTs6FbJl5nd7uxBJktQ3DNskSZKknlf3\nnGwRsUFEjG9l/7iIWL9nypIkSb2tdhjpfvvBKac4jFSSJEnqqq4sfPArYNVW9q9cPSdJkgaQprBt\n2jT45jfnDNteeKHR1UmSJEkDQ1dCtnWASa3snwKs3b1yJElSoyy6KBx11Jxh24orwne/a9gmSZIk\ndaQrIds7wKKt7F8cmN29ciRJUqO1DNtOPtmwTZIkSepIV0K2a4AjI2K+ph0RMT/wk+o5SZI0CLQX\ntj3/fKOrkyRJkvqXroRsBwGrAY9GxBURcQUwjTIn24E9WZwkSWq81sK25ZeHvfaC++9vdHWSJElS\n/1B3yJaZjwHrUnquPQ08DHwPWCszH+3R6iRJUr/RFLY99hgcdhj85S+w5prwiU/AdddBZqMrlCRJ\nkhqnKz3ZyMxXM/OkzNwzM/fNzNMz8+2eLk6SJPU/Cy9chow++iicdRY8/jh8+MMwfjycdx68+26j\nK5QkSZL6XpdCtohYISK+FBEHRcTBtVtPFyhJkvqnUaNg993hrrvgqqtg8cXhC1+AlVeGn/8cZsxo\ndIWSJElS36k7ZIuI3YGHgBOBLwP/U7P9v54sTpIk9X8R8JGPwF//CvfcUz7+/vdhueXggAPK8FJJ\nkiRpsOtKT7YfUeZjWzgz18jMNWu2tXq2PEmSNJCssw787ndlKOk3vwlnnw2rrAK77gqTJjW6OkmS\nJKn3dCVkWxQ4L9PpjSVJUuuWWgqOOKLM13biiXDHHbDJJrDVVnDJJTB7dqMrlCRJknpWV0K2PwLb\n9HAdkiRpEJpvPthnH3jgAfjjH0u49slPwhprwGmnwRtvNLpCSZIkqWd0JWS7Gzg6In4VEftExF61\nWwom8GYAACAASURBVE8XKEmSBr7hw2GXXeCmm+DWW2GDDWDffWH55eEHP4Dnnmt0hZIkSVL3RL2j\nPiPimXaezsxcunsl9Y6IGAdMnjx5MuPGjWt0OZIkDXnTppWhpGecAe++W1YmPeAAWHvtRlcmSZKk\nwW7KlCmMHz8eYHxmTumJc9bdky0zl2pn65cBmyRJ6n9WWglOOAGeeAIOP7ysTrrOOrDDDnDNNeDs\nr5IkSRpIujJcVJIkqccstBAcckjp2XbOOfD007DddrDhhvD738M77zS6QkmSJKljXQrZImKJiNgj\nIn4UEUfVbj1doCRJGhpGjYIvfhHuvBOuvhqWXhq+9KXS4+1nP4OXX250hZIkSVLb6g7ZImJr4CHg\nu8D3gE8C3wC+TjdWHa0WUZgWEW9GxK0RsXE7bb8cETdGxEvV9rf22kuSpIEjArbdFi6/HP71L/jY\nx+CHP4TlloP99is93iRJkqT+pis92X4KnJqZ7wfeAj4BLAfcDPy2K0VExOeAXwCHARsCdwFXRsSi\nbRyyNXA+JdTbDHgCuCoilurK60uSpP5prbXKwgiPP14WRTjvPFh1VfjMZ+C22xpdnSRJktSsKyHb\n2sAZ1cczgXky8xXg+5SebV2xP/DrzDwnM+8H9gbeAPZorXFmfjEzf5WZd2fmg8CXKdeybRdfX5Ik\n9WNLLFEWR3j8cTjlFLjrLthsM/jAB+BPf4JZsxpdoSRJkoa6roRsbwIjq4+fBVauPp4JLF7vySJi\nJDAeuKZpX2YmcDWweSdPM19V00v1vr4kSRo45p0X9t4b7r8fLr4Yhg2D//5vWH31Er69/nqjK5Qk\nSdJQ1ZWQ7Taaw68rgWMi4kDgN8CkLpxvUWA48FyL/c8BS3byHD8DnqIEc5IkaZAbNgx23hluvBFu\nvx022qjM17bMMrDvvnD33Y2uUJIkSUNNV0K2b1PmTAP4ISV0+yrwImXYZk8JIDtsFPEd4LPAJzPz\nnR58fUmSNABsvDFccAE8/DDssw/83//B+uuX4aS/+5292yRJktQ3oozM7GTjiOGUoZ33Z+arPVJA\nGS76BvCpzLy0Zv9ZwNjM3KWdYw8CDgW2zcw7O3idccDkrbbairFjx87x3IQJE5gwYULXL0KSJPUb\n774Ll10Gp58Of/0rzD8/7LYbfOUrMG5co6uTJElSX5s4cSITJ06cY9+MGTO48cYbAcZn5pSeeJ26\nQjaAiHgbWDMzH+mJAqpz3grclpn7VY8DeBw4KTN/3sYx36YEbNtnZofDVJtCtsmTJzPOn7AlSRoS\nHnus9Gb77W/hqadg/HjYay+YMAHe975GVydJkqRGmTJlCuPHj4ceDNm6Mlz0PmC5nnjxGscBe0XE\nlyJiDeBXwLzAWQARcU5EHNXUOCIOBn5CWX308YhYotrm6+G6JEnSALbCCvDjH8Ojj8Kll8JSS8HX\nvlb+/cpXYNIkqPPvjZIkSVKruhKyHQwcGxHbRcRCETGqdutKEZl5EXAgcDhwJ7Ae8NHMnF41WZY5\nF0H4GmU10T8AT9dsB3bl9SVJ0uA2YgTsuCP8+c+ld9vBB8OVV8Imm5QhpKeeCjNmNLpKSZIkDWRd\nGS46u/qw1QMzc3h3i+oNDheVJEm1Zs2Cq64qc7f9+c8wejR87nOlh9tmm0FEoyuUJElSb+mN4aIj\nunDMx3rihSVJkhpp+HD42MfK9vTTcNZZ8JvfwJlnwjrrlLnbvvAFWGihRlcqSZKkgaDTw0Uj4ocR\nMW9mXtne1pvFSpIk9Yall4ZDD4WHHy7DSFdfHQ44oOz/0pfgppucu02SJEntq2dOtsOA+XurEEmS\npEYbNgy23x7+8Ad48kn40Y/gH/+AD34Q1l4bjj8eXnyx0VVKkiSpP6onZHNmEkmSNGQssQQccgg8\n+CBccw2st155vPTSsNtucMMN9m6TJElSs3pXF/VHSUmSNKQMGwYf/jBccAE89RQcdRTccQdssw2s\nsQYceyxMn97haSRJkjTI1RuyPRgRL7W39UqVkiRJ/cBii8GBB8L998P118NGG8H3vw/LLFNWJr3m\nGpg9u8PTSJIkaRCqd3XRw4AZvVGIJEnSQBEBW29dtpNOgt//Hk4/HbbbDlZZBb78Zfh//w+WXLLR\nlUqSJKmvRHZyMpGImA0smZnP925JvSMixgGTJ0+ezLhx4xpdjiRJGmQyyyIJp58OF10EM2fCTjuV\nwG277WDkyEZXKEmSpCZTpkxh/PjxAOMzc0pPnLOe4aLOxyZJktSGCNhySzj7bHj6aTjuuLJowg47\nlMUSvv51uPFGh5NKkiQNVq4uKkmS1MMWWgi+8Q24+26YMgX22AMuu6wML11++TKv26RJrk4qSZI0\nmHQ6ZMvMYQN1qKgkSVIjRMCGG8LPfgbTpsHNN8Muu8C558Imm8D7318WTrj33kZXKkmSpO6qd3VR\nSZIkdcGwYbDFFvDLX8JTT8HVV8M228App8C665btyCPh3/9udKWSJEnqCkM2SZKkPjZiBGy7LZxx\nBjz3HPz5z7DeenD00aV32yablDndnnyy0ZVKkiSpswzZJEmSGmjUKPjEJ+C88+D55+HCC2HZZeHQ\nQ8v8bVtvDaedBtOnN7pSSZIktceQTZIkqZ+Yd1747Gfhj38sPdzOPLPs+8Y3YKml4L/+C846C155\npdGVSpIkqSVDNkmSpH5o7FjYfXe44gp49lk4+WR4662yUukSS5QFFC68EF5/vdGVSpIkCQzZJEmS\n+r1FF4W994brr4cnnoCf/hSefhp23bUEbp//PFx6Kbz9dqMrlSRJGroM2SRJkgaQZZaB/feH224r\nK5Eeeijcey/svDMsuSTsuSf87W8wc2ajK5UkSRpaDNkkSZIGqFVWKSHb3XeXoG3ffeGGG2D77UsY\nt+++cNNNMHt2oyuVJEka/AzZJEmSBoG114af/AQeeggmTYIvfhEuuQQ++EFYcUX49rdh8mTIbHSl\nkiRJg5MhmyRJ0iASARttBMceC489BjfeCDvuCGefXfavvjocckjZ75BSSZKknmPIJkmSNEgNG1Z6\nsp1ySlko4cory+OzzoKtt4bFFoMJE+Dcc+HFFxtdrSRJ0sA2otEFSJIkqfeNGFHmatt++zJH2x13\nwGWXwV/+AhdcUAK5zTaDT3wCPv5xWHfd0itOkiRJnWNPNkmSpCFm2DDYZBP48Y/LPG1PPQWnnw6L\nLw5HHgnrrw8rrABf+1oJ4d54o9EVS5Ik9X+GbJIkSUPc0kvDnnvCn/5Uho1edRXsskv5d8cdYZFF\nSu+2U08t87xJkiRpboZskiRJes/o0fCRj8CJJ8K//w1Tp8IRR8Cbb8J++5WVStddF777XbjpJhdP\nkCRJamLIJkmSpFZFwBprwIEHwrXXwgsvwEUXwfjx8NvflkUUFl8cdtsNzj8fXnqp0RVLkiQ1jgsf\nSJIkqVPGjoXPfKZss2fDpEnNiyecf36Z622LLcrQ0k98AtZe28UTJEnS0NFverJFxD4RMS0i3oyI\nWyNi43barhURf6jaz46Ib/ZlrZIkSUPdsGGw6aZw+OEwZQo8+ST86ldl/rYjjihDSldcEb7+dbj8\n8jLcVJIkaTDrFyFbRHwO+AVwGLAhcBdwZUQs2sYh8wIPA4cAz/RJkZIkSWrTMsvAV74CF19chpX+\n9a+w887l349/vIRvO+5Ygrgnnmh0tZIkST2vX4RswP7ArzPznMy8H9gbeAPYo7XGmXlHZh6SmRcB\n7/RhnZIkSerAmDHw0Y/CSSfBww/DffeVHm+vvQb77gvLLw/rrw+HHgo33wyzZjW6YkmSpO5reMgW\nESOB8cA1TfsyM4Grgc0bVZckSZK6LwLWXBMOOgiuv770crvwwhKy/eY38IEPwGKLlV5vxx0Hkycb\nukmSpIGpPyx8sCgwHHiuxf7ngNX7vhxJkiT1lgUXhM9+tmyzZsHtt8NVV8ENN8D3vgdvvQULLFDC\nt623Ltu4cTByZKMrlyRJal9/CNnaEkA2ughJkiT1juHDYfPNywbw9ttlxdIbbijbj38Mb7wB880H\nW27ZHLptvDGMGtXY2iVJklqKMjKzgQWU4aJvAJ/KzEtr9p8FjM3MXTo4fhpwfGae1EG7ccDkrbba\nirFjx87x3IQJE5gwYUIXr0CSJEm94d13y/DRptDtppvKvG7zzFOCuabQbdNNyzxwkiRJrZk4cSIT\nJ06cY9+MGTO48cYbAcZn5pSeeJ2Gh2wAEXErcFtm7lc9DuBx4KTM/HkHx9YVsk2ePJlx48b1UOWS\nJEnqKzNnwj//2Ry6/f3v8MorMHp0CdqaQrfNN4d55210tZIkqT+bMmUK48ePhx4M2frLcNHjgLMj\nYjJwO2W10XmBswAi4hzgycw8tHo8EliLMqR0FLBMRKwP/CczH+778iVJktTbRoyAjTYq24EHljnd\n7rmnOXQ79VT4yU/K/G0bb9wcum25Jcw/f6OrlyRJg12/CNky86KIWBQ4HFgC+Cfw0cycXjVZFphZ\nc8jSwJ00z9l2ULXdAHy4T4qWJElSQw0fDhtsULb99oPZs+G++5pDt9/+Fo4+urQbP745dPvAB6DF\n7CGSJEnd1i+Gi/YFh4tKkiQNLZnwwAPNodsNN8DTT8OwYSWYawrdPvhBWHjhRlcrSZL60mAeLipJ\nkiT1qAhYY42yffWrJXR7+OHmwO3//g+OP760W3fd5tBtq61gscUaXb0kSRpoDNkkSZI0JETAqquW\nbc89y75HH20O3S67DH75y7J/zTXLvG4bbVSGmm6wgYspSJKk9hmySZIkachaccWy7b57efzEE3Dj\njXDTTTB5MlxwAbzzThliutZaJXBrCt7WX9/gTZIkNTNkkyRJkirLLQe77VY2KAHbv/4Fd9xRQrfJ\nk2HixLJ/+PDWg7d55mnsNUiSpMYwZJMkSZLaMGoUbLhh2b7ylbLvnXfg3nvnDN7OOw/efbcEb2uv\nPWfwtt56Bm+SJA0FhmySJElSHUaNgnHjytbk7bfnDt7OPbc5eFtnnbmDtzFjGncNkiSp5xmySZIk\nSd00enQJz8aPb9739ttwzz1zBm/nnAMzZ8KIEa0Hb6NHN+4aJElS9xiySZIkSb1g9OgSoG20UfO+\nt96aO3g7++zm4G3ddecM3tZd1+BNkqSBwpBNkiRJ6iNjxsDGG5etyVtvwd13NwdvkybBmWfCrFkw\ncuTcwdtaaznHmyRJ/ZEhmyRJktRAY8bAJpuUrcmbb84ZvN12G/zudyV4i4AVV4Q114Q11ij/Nm0L\nL9ywy5AkacgzZJMkSZL6mXnmgU03LVuTN9+Eu+6C++6DqVPh/vvhkkvghBNg9uzSZrHFmgO32gBu\n2WVh2LDGXIskSUOFIZskSZI0AMwzD2y2WdlqvfUWPPRQCd6awrdbby1zvb31Vmkz77zNoVtt+Lbq\nqmW1VEmS1H2GbJIkSdIANmZMmbdt3XXn3D9rFjz++Jzh29SpcMUV8NJLpc3w4bDKKnOHb2usAQss\n0PfXIknSQGbIJkmSJA1Cw4fDSiuVbYcdmvdnwgsvzB2+TZxYQrkmSy/devi21FJlXjhJkjQnQzZJ\nkiRpCIkoc7ctthhstdWcz/3nP/Dgg3OGb9ddB6efDu++W9qMHVvCtpbh28orwwh/u5AkDWF+G5Qk\nSZIEwPzzw7hxZas1cyY88sic4dvUqfDHP8Jrr5U2o0bB+98Pq60GK6ww97bwwvaAkyQNboZskiRJ\nkto1YkQJz1ZbDXbeuXl/JjzzzJzh20MPlXnfHn+8rIjaZL75YPnlWw/gVlihDEMdPrzvr02SpJ5i\nyCZJkiSpSyLK3G1LLw3bbjvnc5kwfTo89lgJ3B57rHm77Ta46CJ4+eXm9iNGwHLLtR3CLbccjB7d\nt9cnSVI9DNkkSZIk9bgIWHzxsm28cettXnttzvCtaXvgAbjqqtJLrtZSS7XfG84VUSVJjWTIJkmS\nJKkh3vc+WGedsrXm7bfhiSdaD+ImTSrPzZzZ3H7BBdsO4FZYoSz24LxwkqTeYsgmSZIkqV8aPRpW\nXbVsrZk1C559tvUQ7ppryr+vv97cfp55mnvCNf279NKlt90SSzT3vJtnnr65PknS4GLIJkmSJGlA\nGj4cllmmbFtsMffzmfDSS62HcFOmwJ/+BC++OPdx73tfc+BWG7619vFCC8GwYb1/rZKk/s+QTZIk\nSdKgFAGLLFK2ceNab/POO/DCC/D882V77rm5P548ufnjd96Z8/gRI8ow1M6EcostBmPG9P51S5Ia\nw5BNkiRJ0pA1alTzCqkdyYRXX209iGv6uGm+uOeeg1demfscCyzQce+4po8XXNA55CRpIDFkkyRJ\nkqROiICxY8u22modt3/nHZg+vf1Q7rbbmh+/++6cx48Y0XEYt9hiJYxbYIFS1+jRvXPtkqSOGbJJ\nkiRJUi8YNap5zriOZJaeb20NWX3+eXjkEbj11vLxjBmtn2f06OYgsGlrCuBa21p7bp557EEnSV1h\nyCZJkiRJDRZRFlFYaCFYffWO27/1VuklN316CdyatldfnfNx0/bMM3M+/5//tH3uESO6Fs7VPjf/\n/C4IIWnoMWSTJEmSpAFmzBhYbrmydcWsWXMHcm0FdE3btGlzt89s/fwRrQdx9QR3CyxQVpCVpIGi\n34RsEbEPcBCwJHAX8I3MnNRO+88AhwMrAg8C38nMK/qgVA1hEydOZMKECY0uQwOY95C6y3tIPcH7\nSN3lPTTwDR/e3HOuq2bPLj3iOhPQNT3/9NMwdSo89dREZs2awIwZJfBry/zzl23MmDKMdZ55evfj\nkSMdKjuQ+F6k/qZfhGwR8TngF8BewO3A/sCVEbFaZr7QSvvNgfOBQ4DLgM8DF0fEhpl5X99VrqHG\nN3F1l/eQust7SD3B+0jd5T0kKMNBF1igbPXaaaeJXHrpBDLhzTfbD+hef70Mj33zzbLVfjxjBjz7\n7Nz7mz5+6636r6k2fOvtUK/pY4fWdo3vRepv+kXIRgnVfp2Z5wBExN7Ax4E9gGNaab8fcEVmHlc9\nPiwitgf2Bb7eB/VKkiRJkropAuadt2xLLdXz58+Et99uPaDrzsczZrT//MyZ9dU5atTc4VtnQrrR\no8sceq1tw4fX/1xXjzEklIqGh2wRMRIYDxzVtC8zMyKuBjZv47DNKT3fal0J7NwrRUqSJEmSBpyI\nEkiNGdO9obH1mjlzzt50PRHsvfpqWW22ZU+9WbPKNnPmnNu77/bd9UY0Jui77z449NDeCQ67El4O\nG+Zw46Gu4SEbsCgwHHiuxf7ngLbW1VmyjfZL9mxpkiRJkiTVZ8SI5vnkGmn27NYDuKatref66pj2\nnmvqEdjeMc8+Cxde2Lna+kprIdz3vgf77993Nahx+kPI1pYA2lirpkvtxwBMnTq1OzVpiJsxYwZT\npkxpdBkawLyH1F3eQ+oJ3kfqLu8hdZf3UP81bFjZRo5sdCUd23//GRx/fMf3UWZz4NgUxDV9PHv2\nnI9r29SGlC2fb6190/laHrPgguDt3v/U5ENjeuqckW2tudxHquGibwCfysxLa/afBYzNzF1aOeYx\n4BeZeVLNvh8BO2fmhm28zueB83q2ekmSJEmSJA1gu2Xm+T1xoob3ZMvMdyNiMrAtcClARET1+KQ2\nDrullec/Uu1vy5XAbsCjQJ1rzEiSJEmSJGkQGQOsSMmLekTDe7IBRMRngbOBrwK3U1Yb/TSwRmZO\nj4hzgCcz89Cq/ebADcB3gMuACdXH4zLzvgZcgiRJkiRJkoawhvdkA8jMiyJiUeBwYAngn8BHM3N6\n1WRZYGZN+1siYgJwZLU9RBkqasAmSZIkSZKkPtcverJJkiRJkiRJA9mwRhcgSZIkSZIkDXSGbJIk\nSZIkSVI3DcqQLSJWiIgzIuKRiHgjIh6KiB9FxMgOjhsdEadExAsR8VpE/CEiFu+rutW/RMShEXFz\nRLweES918pgzI2J2i+3y3q5V/VdX7qPquMMj4unqPexvEbFqb9ap/isiFoqI8yJiRkS8XH1/m6+D\nY65v8T40KyJO7aua1XgRsU9ETIuINyPi1ojYuIP2n4mIqVX7uyLiY31Vq/qneu6hiNi95r2m6X3n\njb6sV/1LRHwwIi6NiKeq+2GnThyzTURMjoi3IuLBiNi9L2pV/1TvPRQRW7fye9gsf58fuiLiuxFx\ne0S8GhHPRcSfImK1ThzXrZ+JBmXIBqwBBPAVYC3KaqV7UxZJaM8JwMeBTwFbAUsD/9d7ZaqfGwlc\nBJxW53FXUBbwWLLaJvRwXRpY6r6PIuIQYF/KisubAK8DV0bEqF6pUP3d+cCawLaU71FbAb/u4JgE\nTqf5vWgp4OBerFH9SER8DvgFcBiwIXAX5T1k0Tbab065z34DbABcDFwcEWv1TcXqb+q9hyozaP7Z\nZ0lghd6uU/3afJTF7PahfE9qV0SsCPwFuAZYHzgROCMiPtJ7Jaqfq+seqiTwfprfh5bKzOd7pzwN\nAB8EfglsCmxH+b3sqoiYp60DeuJnoiGz8EFEHATsnZmt9gaJiAWA6cCumfmnat/qwFRgs8y8vc+K\nVb9S/RXt+MxcuBNtzwTGZuZ/935lGkjqvI+eBn6emcdXjxcAngN2z8yLerdS9ScRsQZwHzA+M++s\n9n0UuAxYNjOfbeO464A7M/OAPitW/UZE3Arclpn7VY8DeAI4KTOPaaX9BcC8mblTzb5bKPfQ1/uo\nbPUjXbiHOv09TkNPRMwGPpmZl7bT5mfAxzJzvZp9Eyk/V+/QB2WqH+vkPbQ1cC2wUGa+2mfFacCo\n/lD0PLBVZt7URptu/0w0WHuytWZBoL2hWuOBEZS/ngCQmQ8AjwOb925pGmS2qbqj3h8Rp0aEP3Cq\n0yJiJcpf3mrfi14FbsP3oqFoc+DlpoCtcjXlL7WbdnDsbhExPSLuiYij2vurnQaPKFNjjGfO95Ck\n3DdtvYdsXj1f68p22msQ6+I9BDB/RDwaEY9HhD0hVa/N8H1I3RfAP6spV66KiC0aXZD6lQUpP0O3\nlwt1+2eiEfXXNfBUcxntC7T3F/0lgXdaSb2fq56TOuMKyhDjacAqwNHA5RGxeQ6VbqPqriUpb/7P\ntdjve9HQtCTlL27vycxZUeb3a+9+OA94DHgaWA84BlgN+HQv1an+Y1FgOK2/h6zexjFLttHe95yh\nqSv30APAHsDdwFjg28A/ImLtzHyqtwrVoNLW+9ACETE6M99uQE0aWJ6hTLVyBzCaMnXU9RGxSWb+\ns6GVqeGqHtknADdl5n3tNO32z0QDKmSLiKOBQ9ppksCamflgzTHLUIKPCzPzd115WTo/Blz9XFfu\noXq0GMr3r4i4B3gY2Aa4rivnVP/T2/dRWy+L70WDRmfvofZOQTv3Q2aeUfPwXxHxLHB1RKyUmdPq\nKlaDRb3vIb7nqKU274nMvBW49b2GZWjNVGAvyrxuUldE9a/vRepQ9XN37c/et0bEKpT52V1EQ6dS\n5uvfsgvH1vUz0YAK2YBjgTM7aPNI0wcRsTRlXPZNmfnVDo57FhgVEQu06M22OHMnmRq46rqHuisz\np0XEC8CqGLINJr15Hz1LeSNfgjnfexYH7mz1CA1Enb2HnqV87t8TEcOBhajve9NtlPtqVUpPWw1e\nLwCzKO8htdr7eebZOttrcOvKPTSHzJwZEXdS3nOkzmjrfejVzHynAfVocLidroUqGkQi4mRgB+CD\nmflMB827/TPRgArZMvNF4MXOtK16sF0LTKJ0X+/IZGAmZfW2poUPVgOWB27pSr3qf+q5h3pCRCwL\nLELpvqxBojfvoyqYfZbyXnQ3vLfwwabAKb3xmup7nb2Hqt4gC0bEhjXzsm1LCcxuq+MlN6T8Bc73\nokEuM9+NiMmU++RSeG+IxLbASW0cdksrz38Ef/4Zkrp4D80hIoYB6wCX91adGnRuAT7WYt/2+D6k\n7tkAf/YZ0qqAbWdg68x8vBOHdPtnokG58EFELAVcT1m04GBg8YhYIiKWqGmzdERMjYiN4L2JxX8L\nHBcR20TEeEovg5tdWXRoiojlImJ9yhL0wyNi/Wqbr6bN/RGxc/XxfBFxTERsGhErRMS2lCV/H6RM\nlqghqN77qHIC8P2I2DEi1gXOAZ4ELunT4tVwmXk/5f3jNxGxcURsSVmKfGLTyqItv59FxMoR8f2I\nGFe9F+0EnA3ckJn3Nupa1KeOA/aKiC9VK9T+CpgXOAsgIs6JiKNq2p8IfCwiDoiI1SPiR5SJ70/u\n27LVj9R1D0XEDyLiIxGxUkRsSJkXcgXgjLlPraGg+rl4/YjYoNq1cvV4uer5oyPi7JpDfgWsEhE/\nq96Hvk6ZR/S4Pi5d/US991BE7BcRO0XEKhGxdkScAHwIv5cNWRFxKrAb8Hng9aZMKCLG1LQ5u6d/\nJhpQPdnqsD2wcrU9Ue1rGkc7vHo8kjIJ9Lw1x+1P6R7/B8pkiX8F9umDetU/HQ58qebxlOrfDwE3\nVh+/nzLBL5R7Z73qmAUpE45fCfwwM9/t9WrVX9V7H5GZx0TEvMCvKffS3ynL2jtcYmj6POUb+9XA\nbMr3qP1qnm/5/ewdYLuqzXyU74P/CxzZR/WqwTLzoijL1B9OGfLwT+CjmTm9arIspfd+U/tbImIC\n5R45EngI2LmDiYE1iNV7D1GGsJ9OmRj6ZcoIkc2rPxRoaNqIMlVKVtsvqv1nU0YZLQks19Q4Mx+N\niI9TQrVvUv64uGdmtlzlT0NHXfcQMKpqszTwBmVEyLaZeSMaqvam3DvXt9j/P5RODFDuoVlNT/TE\nz0ThgoeSJEmSJElS9wzK4aKSJEmSJElSXzJkkyRJkiRJkrrJkE2SJEmSJEnqJkM2SZIkSZIkqZsM\n2SRJkiRJkqRuMmSTJEmSJEmSusmQTZIkSZIkSeomQzZJkiRJkiSpmwzZJElSw0XELRFxVKPrUN+K\niLUj4vaIeCsi/tGD5x0w91NEfDQiZkXEqEbX0p6IeCYi9qqj/eoRMTsiVuvNuiRJ6k8M2SRJkbn9\n1AAADTtJREFU6kURsURE/DIiHq6ChMci4tKI+HBNm0erX0ZnR8QbETEtIi6MiA+1cc7dq2Di9Yh4\nNSKuj4iPt1PD1tW5Z9W8Tu02KyK26o3rb6SIGF1d3/aNrmWwqAKhpntmVkS8EhGTI+KoiFi8C6c8\nEngeWAXYoWerbdbZgCginq35upgZEU9GxK8j4n29VRtwDbBUZr7T0yeOiIkRcX4r+5s+j/UEe+sA\nZ9dZQnZQ31cj4pk6zylJUr9lyCZJUi+JiBWAKcA2wEGUX1L/C7gOOLmmaQLfB5YEVgO+CLwCXB0R\n321xzmOB04CJwLrAxsBNwCUR8fU2Srm5OvdS1b8XAVcAS9Tsn6sXUUSMrPOS1Yca+PlJYAXKfbMR\ncCzwceCeLvRaWgX4e2Y+lZmv9GyZXZLAtylfF8tRvhY/QrnGLmvrcxURIzJzZmY+3xvn70C7Adhc\njTNfzMy3u/A67Yl665AkqT8zZJMkqfecBswCNs7MP2XmvzNzamYeD2zWou1/MvP5zHwyM2/KzK8C\nPwEOj4j3A0TEZsABwEGZeXxmPpKZD2Tm94ETgOMiYpmWRTT9Et+0AW8Cb2fm9Jr9MyPi6GqY3dci\nYhrwcvW6n4iIm6teS9Mj4uIqQKR6vmlY2I4RcWPVw25KRIyvraPqUdf0/IsRcVlEzFvTZEREHBcR\nL0fEUxHxnRbHLxwRZ1U1vBIRV0XEWl35xNScc9eIuC8i3q56G36jxfPfioh/V70Qn42Ic2uemxAR\n90bEm1VNf20t7IiI4RHxXER8qcX+LareUkt05vra+fy0WUe0MmwyIq6IiFM7c43taLpv/p2ZE4Et\ngNeYMzymqvX+qrZ/RcSXq/2jI2I2sBZwdNUr7uDqueMi4sEovTr/HRE/iIhhNeecq3dWRJwWEVe0\nVmhE3EIJlE+r7tM3Ori216preyYzrwPOB8bVnG/xKD1Nn6zu5X9GxH+3fM2I+EVEnBwRLwIXR3PP\nyj2re/8/wAHRSq+yiPhQ9TX3RpSersdGxJia55+JiEMi4ryIeBU4sYNr6lAnX3OvmsdrV9f5ZkTc\nHREfidZ7jq4erbwvRMRHgVOBJaK5d+TB3b0OSZIayZBNkqReEBELAR8FTs7Mt1o+n5mvduI0J1K+\nV+9cPZ5ACTJOb6XtL4BRwKe6VHCztSm97XYCNq32zQv8FNiQ0qtnJPCHVo49AjgcWB94HDiv6YmI\n2BS4CrgD2AT4IPBXYHjN8V8BnqP0jvohcFREbFnz/J+qWrar2kyl9PabvysXGhFbAOcCZ1bXfRRw\nTER8tnr+A8DPgIOB91P+X/5RPbc8cA4lVFoN+BDw59ZeJzNnUXoP7tbiqQnA1Zn5XDvXd02L65vj\n81NPHW38H7R5jfXIzNeB3wAfiogFqnPvCRxC6cW5BuVzekxEfKbqEbUk8DDlvlkK+GV1upeBL1TH\nHADsC7TVS3OOMtrYvwMwnXKNS1J64XVKRCxXHX9rze55KL1DP0bpnXoWcEFErNfi8C8DL1G+jvar\n2X84Jbhbm+avkfdqj4g1gUsp9+balPtmO8rXeK2Dq7rWB47p7DU1vcwcDzr/mk3th1ftnwfGA/tQ\n3iNafg6Ctt8XrqXcH9MpIWjtPSBJ0oA0otEFSJI0SK1K+QXzga6eIDNfjojngRWrXe8HHs7Mma20\nfSYiZlCClu4YBnwhM1+rOfdFtQ0i4qvA4xGxcmY+UvPU0Zl5ddXmx8AdEbF8Zj5OCQRuyMwDatrf\n1+K1b8/Mn1UfPxwR3wS2BW6OiO2ANYEPV6EVEfEtYBfgk5RwoF4HAH/JzJ9Xj/9dBSXfpoRiywEz\ngMuroPQJ4J9V22Uon98/Vr0DnwDubee1zgNujIjFM/P5KqT4DCWAoo7rm+PzExGb11lHS+1dY73u\nr+pbvqrhR8C+mfmX6vnHImIDYG/gf6v/h1lUvTibTpKZP6k55+MRsS7wWVr0kuus6utoNlUPtU4c\nckJE/IISAI8B/g6816syMx8DTmrR/uPAp4G7a/bfm5k/bHoQEaOrD8/MzNoAep0Wr38ocEZmnlY9\nnhYRBwKXR8Q3MnN2tf+KzOxMKPXpiNixxb7hLR539jWb7EgJxcY3DfONiB9SgreW2nxfqHrhzc7M\n6Z24DkmS+j17skmS1Duaeop0d76heuYs6on5jR6uDdjgveGgF0bEI9UvxVOr11m+plkC99Q8fqaq\np2ky/A0oE7y35+4Wj5+pOX49YGHglYh4LSJeA16l/KK/SqeubG5rUnok1bqZ0oMK4HJKL5tHowzj\n3LUmKJlEmQvvgYi4ICL2aOrB1ZrMvJXSi2fXatf2wPuAi+u8vpafn7rqaEV711iv9+75qifnMsC5\nTddTXdOBwErtniTiCxHxjyhDV1+jzFe4fHvH9LAjKL2u1qX03JyPmvAoIkZExI8j4p4ow55fA7Zq\npcY72jj/5A5ef33gqy3+3y6hBGPL1XGeJn+l3F/r12wtewZ29jWbrAY80mIevdtp0UOOjt8XJEka\nVOzJJklS73iI8gtm0zCsukXEwsBiQFNvsQeBLaOaLL1F26WABao23fF6K/uuoPRM+h/KL8nzUX7B\nb7ky4bs1HzeFfU1/0HuzE6/9bovHWXP8/MA0SjjV8hf5lztx7ta0Fkq+d+7MnFH1bPswJWw5EvhB\nRGxSDY/cphrOuj2wP3BERGyUmU+38XrnA5+n9IKaAFyamf+p8/rm+PxU90F7dcxu5Xwja47v6Brr\nsVb1eo8DC1X7vgTc1aLdXD0xm0TENpThu9+hDCd8Ffh/wJ41zWYz9x+Ke3IRiBdqemg+XPXoui4i\ntsjMf1BCv70oQ0CnUj4nv2Lur4e2/v86+n+dnzJs8tetPPdkHedp8p/MnFa7I6p5Hrvwmu+dgna+\ndlpo731BkqRBxW9wkiT1gsx8GbgS2Cci5mn5fESM7cRpvkVZOOGS6vEFlF+Gv9pK228D7wB/7FLB\nbYiIpSnDVX+cmTdk5oPAItTfY+5uytDPrpoCLAu8VS34ULt1NWS7D/hAi31bUoIToMynlpl/y8yD\nKZPfr0GZT67p+Zsz8zDKfHXDKXOlteU8YOMq1Go5xLVb19dOHdMpveGA91ahXKvFse1eY2dU88bt\nCfyt6mn3BPACsHIr1/N4O6faArg/M3+RmXdm5sPM3fNtjmuqbNBBie8w9xDJzmoaKtn0dbwF8IfM\nvCgz76GEii1Dq+6YAqzVyv/bI01DiXtBva95P7BK1WOxycbU/77Qnc+LJEn9jj3ZJEnqPV+nDD+8\nPSIOowRNIyg9jr5KmWC8yfuirDI5khIqfBHYA/hOU6+azLw1Ik4Cfl4N6bu4av9F4BvAfpn5VA9f\nw3TKnF17R8TRlKGLP22lXVu9WJocCUyJiOOBMyjBxbbA2S2Hp7bhcspcYZdExHcpE+YvC3wCODcz\n25uHbJWIWL/FvgeAY4G/Vysa/hHYhjJZ/e4AEbELJcy5ifJ/sAsl9HyoWjBgC+BqSpi0JbAgNQFd\nS5n5QETcCZwNvE0JYbt1fe3U0TTf3bWUFWq3p4RBh1AWV2g6vs1rbOs6KJ/rJSPibUrvyY2r884D\nfLO61qzm3zoqymqeV1PmN9sEGJOZp7Rx7oeAVaOs1vnPqp4dgNrFQ66lhNefo4RD/0OZA7G9+dYe\npfT4u5iysu5L7bRdoPpaDErAfDSlB+ftNTX+V0RsAvyHMt/gQq2cp6uOosxDeBxlUYU3KQssbJWZ\n+/fg63TnNS+j/J+cXd2viwCHVc/VBm0dvS88Cixc3cdTgddbWyhGkqSBwp5skiT1ksx8lNIz6DpK\noHMPZYXNDwFfa9H8cOBpyi/w51Dm6/pwZh7b4pz7U8K7XavzTaL0xto5M0/thWt4t3qtLSlDRo+m\nzKs1V9P29mXmvygrV25a1fx3yuqrs1q2beP42ZRw8nbK/89U4PeUVQnbmzQ9KRPmT2mxrVXNk7Yb\nJVS7F/gu8O3M/N/q2JeBz1FCnX9RwsxPV72rXqGEhFdUtXwf+Hpm3tBOLVB6s61Hmfj/vWGT3bi+\ntuq4sXr+V8CFlKGq11KCq9rVQ9u7xrYkZWjrU5TP5YGUFU3Xy8x/11zTKZSVQfeiBMzXUobLTmtx\nLmqO+V/gNMqwxSmUucKOatHmUspqmicAt1CCnImt1Fjre5Sh29NoffhjrZ9Rvhafoqz4+gKwfU0Y\nfBjVyrbA3yhfs5d38Pod7W9ukDmFEviuSwk/76B8Xp+o5zz1qPc1q3t3J2DRqu3JwE8on4u3Wjum\njfNcRwn1LqaEpN/s7rVIktRIkdmj36MlSZIkDTERsS3ljwjLtTMvoSRJg5rDRSVJkiTVJSI+DbxE\nGdq8BnAicLUBmyRpKDNkkyRJklSvsZTh48tQhjT/lTI/nSRJQ5bDRSVJkiRJkqRucuEDSZIkSZIk\nqZsM2SRJkiRJkqRuMmSTJEmSJEmSusmQTZIkSZIkSeomQzZJkiRJkiSpmwzZJEmSJEmSpG4yZJMk\nSZIkSZK6yZBNkiRJkiRJ6iZDNkmSJEmSJKmb/j/n4BBQb/dPKgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ff015f8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "fig.suptitle('CDO Tranche Survival Function', fontsize=14, fontweight='bold')\n",
    "ax = fig.add_subplot(111)\n",
    "ax.set_xlabel('CDO Tranche Loss versus Default Barrier Height')\n",
    "ax.set_ylabel('Tranche Survival Function')\n",
    "ax.plot(x,QQ)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "# With a survival function one can calculate the CDO spread for a single tenor CDO\n",
    "\n",
    "## For a multi-tenor CDO one needs to create an array of cashflows and calculate C($T_i$) \n",
    "## Notice that this is not what we did above. Here we calculate the survival probability as a function of changing upwards the barrier, that is, making easier to default!!\n",
    "## C($T_i$) should be an ever decreasing array, since the probality of survival on later years is smaller than the probability of survival in the first year."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    ""
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python [Root]",
   "language": "python",
   "name": "Python [Root]"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3.0
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}